DLMF:29.11.E1 (Q8721): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12351 / rank
 
Normal rank
Property / Symbols used: Q12351 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q12351 / qualifier
 
xml-id: C29.S1.XMD9.m1dec
Property / Symbols used
 
Property / Symbols used: Q12383 / rank
 
Normal rank
Property / Symbols used: Q12383 / qualifier
 
Defining formula:

ω 𝜔 {\displaystyle{\displaystyle\omega}}

\omega
Property / Symbols used: Q12383 / qualifier
 
xml-id: C29.S11.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12352 / rank
 
Normal rank
Property / Symbols used: Q12352 / qualifier
 
Defining formula:

w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}}

w(z)
Property / Symbols used: Q12352 / qualifier
 
xml-id: C29.S2.XMD1.m1dec

Latest revision as of 01:25, 2 January 2020

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DLMF:29.11.E1
No description defined

    Statements

    Defining formula
    d 2 w d z 2 + ( h - ν ⁢ ( ν + 1 ) ⁢ k 2 ⁢ sn 2 ⁡ ( z , k ) + k 2 ⁢ ω 2 ⁢ sn 4 ⁡ ( z , k ) ) ⁢ w = 0 , derivative 𝑤 𝑧 2 ℎ 𝜈 𝜈 1 superscript 𝑘 2 Jacobi-elliptic-sn 2 𝑧 𝑘 superscript 𝑘 2 superscript 𝜔 2 Jacobi-elliptic-sn 4 𝑧 𝑘 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}+(h-\nu% (\nu+1)k^{2}{\operatorname{sn}^{2}}\left(z,k\right)+k^{2}\omega^{2}{% \operatorname{sn}^{4}}\left(z,k\right))w=0,}}
    0 references
    DLMF id
    DLMF:29.11.E1
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2adec
    0 references
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    Q12348
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1dec
    0 references
    Q12349
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C29.S1.XMD7.m1dec
    0 references
    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1dec
    0 references
    Q12351
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C29.S1.XMD9.m1dec
    0 references
    Q12383
    Defining formula
    ω 𝜔 {\displaystyle{\displaystyle\omega}}
    xml-id
    C29.S11.XMD1.m1dec
    0 references
    Q12352
    Defining formula
    w ⁢ ( z ) 𝑤 𝑧 {\displaystyle{\displaystyle w(z)}}
    xml-id
    C29.S2.XMD1.m1dec
    0 references
     
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